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1. For the integral OA. x = 3 sec (0) OB. x = 3 tan(0) OC. None of these OD. x = 3 sin(0) OE. x = 3 tan(8) da x²√x² +9 the appropriate substitution is ..... and the resulting trigonometric integral is fsec (0) do sec (0) tan² (0) S -do -do tan (0) do .....

1. For the integral OA. x = 3 sec (0) OB. x = 3 tan(0) OC. None of these OD. x = 3 sin(0) OE. x = 3 tan(8) da x²√x² +9 the appropriate substitution is ..... and the resulting trigonometric integral is fsec (0) do sec (0) tan² (0) S -do -do tan (0) do .....

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem:** 1. For the integral \( \int \frac{dx}{x^2 \sqrt{x^2 + 9}} \), the appropriate substitution is ..... and the resulting trigonometric integral is ..... **Options:** - **A.** \( x = 3 \sec(\theta) \) \[ \frac{1}{9} \int \sec(\theta) \, d\theta \] - **B.** \( x = 3 \tan(\theta) \) \[ \frac{1}{9} \int \frac{\sec(\theta)}{\tan^2(\theta)} \, d\theta \] - **C.** None of these - **D.** \( x = 3 \sin(\theta) \) \[ \frac{1}{3} \int \frac{1}{\sin(\theta)} \, d\theta \] - **E.** \( x = 3 \tan(\theta) \) \[ \frac{1}{9} \int \frac{1}{\tan(\theta)} \, d\theta \]
Transcribed Image Text:**Problem:** 1. For the integral \( \int \frac{dx}{x^2 \sqrt{x^2 + 9}} \), the appropriate substitution is ..... and the resulting trigonometric integral is ..... **Options:** - **A.** \( x = 3 \sec(\theta) \) \[ \frac{1}{9} \int \sec(\theta) \, d\theta \] - **B.** \( x = 3 \tan(\theta) \) \[ \frac{1}{9} \int \frac{\sec(\theta)}{\tan^2(\theta)} \, d\theta \] - **C.** None of these - **D.** \( x = 3 \sin(\theta) \) \[ \frac{1}{3} \int \frac{1}{\sin(\theta)} \, d\theta \] - **E.** \( x = 3 \tan(\theta) \) \[ \frac{1}{9} \int \frac{1}{\tan(\theta)} \, d\theta \]
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integral fraction numerator d x over denominator x squared square root of x squared plus 9 end root end fraction

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